The invention relates generally to a method of tracking the motion of the elements of a human tissue which is deformed during a respiratory cycle using ARMA modeling and using this tracking to target therapeutic thermal energy on a diseased portion of the tissue through multiple respiratory cycles. The thermal treatment, particularly the thermal ablation, of lesions, tumors or other diseased tissue has been practiced for some time. More recently high intensity focused ultrasound (HIFU) has been used to reach internal tissue using magnetic resonance imaging (MRI) to locate the appropriate focal point for the HIFU. In such applications MRI has been used to create thermal maps so that the effect of the application of the HIFU can be tracked and adjusted in real time with the aim that the diseased tissue is ablated while the healthy surrounding tissue is not adversely affected. A difficulty has arisen in applying this technique to tissue that is subject to displacement and elastic deformation during a respiratory cycle. One approach has been to gate the application of thermal energy such as HIFU so that it is only applied at a particular point in the respiratory cycle and assume that a given element of a tissue of a quiescent subject will return to the same location at a given point in the respiratory cycle. Another approach has been to track the portion of a tissue that is the object of thermal treatment in real time as the thermal energy is being applied. However, this requires frequent cycling of the MR apparatus between mapping the location of the portion of the tissue under treatment and thermal mapping to monitor the result of applying the thermal energy. Both of these approaches cause a significant lengthening of the time of treatment because for significant periods during the overall treatment thermal energy may not be appropriately applied. One needs to await a given window in the respiratory cycle or the availability of the MR apparatus for thermal mapping.
Yet another approach has been to develop a mathematical model, which predicts the locations of the elements of a given tissue subject to displacement during respiration so that the location of an element that is the target of thermal treatment can be predicted throughout a respiratory cycle. The model is developed by observation of the tissue of interest through multiple respiratory cycles. However, these models have been developed using a harmonic motion approach. Such models do not have adequate predictive power for tissues that undergo elastic deformation through a respiratory cycle and do not deal with changes in the elastic properties of the element of a tissue undergoing treatment. For instance a lesion being subjected to thermal ablation typically becomes stiffer and thus exhibits changes in its elastic behavior as treatment progresses.